Direct numerical simulation is what it say, the simulation of flow directly using the navier stokes equations without the need for turbulence models and the like. This is done by the reduction of mesh size to such a level that the turbulence in the flow can be directly modelled using the navier stokes equations. this means that the mesh is getting so small that it is approaching the theoretical "infinately small control volume" This way the N-S can be solved directly. As you may imagine with such a small mesh you need one hell of a big computer, a lot of time and even more patience. It does mean, however, that your results are very accurate.

One comment: the mesh does NOT get so small that it approaches the "infinitely small control volume". Rather the control volume size is dictated by the Kolmogorov length scale, which is a function of Reynolds number.